Linear Differential Equations for a Fractional Spin Field

Abstract

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional nonunitary representations of that group, $0<2j\in Z$, they are transformed into equations for spin-$j$ fields. A local gauge symmetry associated to the vector system of equations is identified and the simplest gauge invariant field action, leading to these equations, is constructed.

15 pages, LATEX, revised version of the preprint DFTUZ/92/24 (to be published in J. Math. Phys.)

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